In a solid-oxide fuel cell system, a fuel/air manifold conveys air and tail gas fuel from the anodes in a fuel cell stack assembly to a tail gas combustor, producing a heated combustor exhaust having the highest mass flow in the system. The exhaust is passed through a heat exchanger to warm incoming cathode reaction air, and the exhaust is partially cooled by the exchange. From the heat exchanger, the exhaust gas is passed through a tempering jacket space surrounding the fuel cells in the stack. During start-up of the system, the exhaust gas is hotter than the stack and so the warm-up period is shortened. During normal operation of the system, the exhaust gas is cooler than the operating temperature and therefore cooling of the stack is assisted by contact with the exhaust gas.